My research interests are in geometric analysis and probability. Recently, I
have worked mainly in the overlap of these two fields, using Brownian motion as
a tool in geometry. For example, I have been studying the relationship of
heat kernel asymptotics to geodesic geometry, global aspects of minimal
surfaces, and solvability of the Dirichlet problem at infinity.
Below is a list of publications and preprints, most with links to the paper
in some form.
Small time heat kernel asymptotics at the sub-Riemannian
cut locus (with D. Barilari and U. Boscain).
Stochastic methods for minimal surfaces, accepted
to the proceedings volume for the Santaló Summer School on
Geometric Analysis.
A preprint can be downloaded from the conference
website.
On parabolicity and area growth of minimal surfaces,
to appear in the Journal of Geometric Analysis.
E-print, from
Springer's Online First service.
Brownian motion and the Dirichlet problem at infinity on
two-dimensional Cartan-Hadamard manifolds.
Brownian motion and the parabolicity of minimal
graphs.
A martingale approach to minimal surfaces,
J. Funct. Anal.
256 (2009), no. 8, 2440-2472.
Electronic
reprint,
courtesy of
the Journal of Function Analysis and ScienceDirect (subscription required).
The small-time asymptotics of the heat kernel
at the cut locus, Comm. Anal. Geom.
15
(2007), no. 4, 845-890.
Electronic
reprint,
from Communications in Analysis and Geometry.
Analysis of the cut locus via the heat kernel
(with D. Stroock), Surveys in Differential Geometry, Vol. 9,
International Press, Boston (2004), 337-349.
Equilibrium configurations for a floating drop
(with A. Elcrat and D. Siegel), J. Math. Fluid Mech.
6 (2004), no. 4, 405-429.
Electronic
reprint,
from SpringerLink (subscription required).
C-singular solutions of the capillary problem
(with R. Finn), J. Reine Angew. Math.
512 (1999),
1-25.